Consistent Interactions between Gauge Fields and Local BRST Cohomology : The Example of Yang-Mills Models

TL;DR

This paper uses BRST cohomology to analyze the interactions in Yang-Mills models, confirming the uniqueness of the gauge coupling and the necessity of the Jacobi identity for consistency.

Contribution

It demonstrates how local BRST cohomology techniques can derive the uniqueness and consistency conditions of Yang-Mills interactions.

Findings

Unique local cubic vertex for gauge fields identified

Second-order consistency requires structure constants to satisfy Jacobi identity

Re-derivation of Yang-Mills coupling uniqueness through cohomological methods

Abstract

Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the Yang-Mills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincar\'e invariant cubic vertex for free gauge vector fields which preserves the number of gauge symmetries to first order in the coupling constant; and (ii) that consistency to second order in the coupling constant requires the structure constants appearing in the cubic vertex to fulfill the Jacobi identity. The known uniqueness of the Yang-Mills coupling is therefore rederived through cohomological arguments.